We will make use of the
following theorem on the existence of a solution of a linear integral
equation [1]}.
[[1]}] Let \(\mathcal {X}\)  and \(\mathcal {Y}\)  be Hilbert spaces.
Let \(E:\mathcal {X}\rightarrow \mathcal {Y}\)  be a compact linear operator with singular system \(\lbrace (\mu _{n},\varphi _{n},g_{n})\rbrace _{n=1}^{\infty }.\) 
The equation of the first kind
\(E\varphi =f\) 
